<h2>题目编号 : 163</h2>
<div style="color:#666;font-size:80%;">13 October 2007</div><br />
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<p>Consider an equilateral triangle in which straight lines are drawn from each vertex to the middle of the opposite side, such as in the <i>size 1</i> triangle in the sketch below.</p>
<div style='text-align:center;'><img src='project/images/p_163.gif' width='300' height='200' alt='' /></div>
<p>Sixteen triangles of either different shape or size or orientation or location can now be observed in that triangle. Using <i>size 1</i> triangles as building blocks, larger triangles can be formed, such as the <i>size 2</i> triangle in the above sketch. One-hundred and four triangles of either different shape or size or orientation or location can now be observed in that <i>size 2</i> triangle.</p>
<p>It can be observed that the <i>size 2</i> triangle contains 4 <i>size 1</i> triangle building blocks. A <i>size 3</i> triangle would contain 9 <i>size 1</i> triangle building blocks and a <i>size n</i> triangle would thus contain <i>n<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> size 1</i> triangle building blocks.</p>
<p>If we denote T(<var>n</var>) as the number of triangles present in a triangle of <i>size <var>n</var></i>, then</p>
<p style="margin-left:50px;">T(1) = 16<br />
T(2) = 104</p>
<p>Find T(36).</p>

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